Mathematical Statistics STAT 710
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Mrs. Triston Collier
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This 1 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 710 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/205090/stat-710-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
TA Yuan Jiang Email jiangy statwiscedu STAT 710 Discussion 21 April 157 2008 1 Likelihood Ratio Tests Example 1 Let X 7 Xmi 239 17 27 be two independent random samples from the uniform distributions on 017 239 17 27 respectively7 where 91 gt 0 and 02 gt 0 are unknown i Find an LR test of size a for testing H00102 versus H1 1917392 ii Derive the limiting distribution of 72 logA when 711712 a H E 07 oo7 where A is the likelihood ratio in part Example 2 Let X1L7 7 X be a random sample from a population having the Lebesgue density 7 61 02 1e m91 z gt 0 f9192 61 62716w92 x S 07 where 91 gt 0 and 02 gt 0 are unknown Find an LR test of size a for testing H0 91 02 versus H1 91 31 02 Discuss the limiting distribution of 72 log A where A is the likelihood ratio 2 Wald s and Rao s Tests Example 3 Suppose that X X1L7 Xk has the multinomial distribution with a known size n and an unknown probability vector 1017 pk Consider the problem oftesting Ho 3 1017 pk 1001100k versus H1 p177pk 7 11901H3900k7 where 10017 7p0k is a known probability vector Find the forms of Wald7s test and Rao7s score test Of ce 1275A M80 1 Phone 262 1577